In the exercises, from 1 to 7, find the value of the expression:

1. \[ (81)^{1/4} \]
2. \[ 8^{4/3} \]
3. \[ (25)^{3/2} \]
4. \[ (25)^{-3/2} \]
5. \[ \left( \frac{1}{8} \right)^{-2/3} \]
6. \[ \left( \frac{27}{16} \right)^{-1/2} \]
7. \[ (0.01)^{-1} \]

In the exercises, from 8 to 13, simplify the expression:

8. \[ \left( \cfrac{ \mathrm{e}^7 }{ \mathrm{e}^3 } \right)^{-1} \]
9. \[ \cfrac{ 3^3 3^5 }{ \left( 3^4 \right)^3 } \]
10. \[ \cfrac{ 5^{1/2} \left( 5^{1/2} \right)^5 }{5^4} \]
11. \[ \cfrac{ 2^{-3}2^5 }{ \left( 2^4 \right)^{-3} } \]
12. \[ \cfrac{ \left( 2^4 \right)^{1/3} }{ 16 \left( 2^{7/3} \right) } \]
13. \[ \cfrac{ \left( 2^{1/3} 3^{2/3} \right)^3 }{ 3^{5/2} 3^{-1/2} } \]

In the exercises, from 14 to 19, solve the equation.

14. \[ 2^{2x-1} = 8 \]
15. \[ \left( \frac{1}{3} \right)^{x+1} = 27 \]
16. \[ 8 \sqrt[3]{2} = 4^x \]
17. \[ \left( 3^{2x}\, 3^2 \right)^4 = 3 \]
18. \[ \mathrm{e}^{-6x+1} = \mathrm{e}^3 \]
19. \[ \mathrm{e}^{x^{2}-2x} = \mathrm{e}^3 \]

In the exercises, from 20 to 28, sketch the graph of the function. Use the translation and reflection techniques in all of them, except for the exercises 25 and 27.

20. \[ y = \mathrm{e}^{x+2} \]
21. \[ y = -2\mathrm{e}^x +1 \]
22. \[ y = \mathrm{e}^{-x} \]
23. \[ y = \mathrm{e}^{-x}+2 \]
24. \[ y = 2-\mathrm{e}^{-x} \]
25. \[ y = 3^x \]
26. \[ y = 3^{-x+2} \]
27. \[ y = 4^x \]
28. \[ y = -4^{-x-1} \]
29. If   \(g(x)=A\mathrm{e}^{-kx}\),   \(g(0)=9\)   and   \(g(2)=5\),   find \(g(6)\).
30. If   \(h(x)=30-P\mathrm{e}^{-kx}\),   \(h(0)=10\)   and   \(h(3)=-30\),   find \(h(12)\).